Reachability relations of timed pushdown automata

Timed pushdown automata (tpda) are an expressive formalism combining recursion with a rich logic of timing constraints. We prove that reachability relations tpda expressible in linear arithmetic, generalising Presburger arithmetic and rational arithmetic. The main technical ingredients novel quantifier elimination result for clock constraints (used to simplify the syntax transitions), use difference express fractional values, application Parikh's theorem reconstruct integral values.